Chemo-mechanics in alloy phase stability

We describe a first-principles statistical mechanics method to calculate the free energies of crystalline alloys that depend on temperature, composition, and strain. The approach relies on an extension of the alloy cluster expansion to include an explicit dependence on homogeneous strain in addition to site occupation variables that track the degree of chemical ordering. The method is applied to the Si-Ge binary alloy and is used to calculate free energies that describe phase stability under arbitrary epitaxial constraints. We find that while the incoherent phase diagram (in which coexisting phases are not affected by coherency constraints) hosts a miscibility gap, coherent phase equilibrium predicts ordering and negative enthalpies of mixing. Instead of chemical instability, the chemo-mechanical free energy exhibits instabilities along directions that couple the composition of the alloy with a volumetric strain order parameter. This has fundamental implications for phase field models of spinodal decomposition as it indicates the importance of gradient energy coefficients that couple gradients in composition with gradients in strain

Modeling Defect Mediated Dopant Diffusion in Silicon.

The current understanding of dopant diffusion in silicon comes from the synthesis of experimental and computational research. Dopant diffusion is mediated by defects, and the relevant physical phenomena range over many time and length scales, necessitating a multi-scale modeling approach. In this work, we focus on two essential aspects, (1) the accuracy of atomistic methods for calculating defect parameters, and (2) an accelerated kinetic Monte Carlo (KMC) method, which we use to investigate the effects of percolating dopant-defect interactions on diffusion. We use continuum linear elasticity to quantify the effects of boundary conditions on atomistic calculations of defect energies and volume tensors. It predicts that when using periodic boundary conditions with zero average stress, energies converge with the inverse of system size and relaxation volume tensors are independent of supercell size or symmetry. We verify the linear elastic prediction in the far field of atomistic calculations by calculating the formation energy and volume tensor for vacancy and interstitial defects in silicon using the Stillinger-Weber empirical potential. In practice, both defect energies and relaxation volume tensors converge with the inverse of system size because changes in the bonding at the defect affect the elastic moduli. We also introduce an accelerated KMC method which automatically determines which states comprise trapping energy basins, allowing simulations to reach very long times compared to standard KMC simulations. We validate the accelerated method by performing simulations of V-As cluster dissolution and comparing to standard KMC simulations. Then we apply the method to highly time and concentration dependent vacancy-mediated As diffusion in Si. At high As concentrations, percolating dopant interactions lead to limited increased diffusivity, but the effect is limited in magnitude and duration as immobile clusters form quickly. The energy basin algorithms for accelerating KMC simulations may be very useful in a wide variety of applications. By considering issues such as grouping isolated diffusing species and collecting data when the exact location of the system within an energy basin is not resolved, we provide an example that can be followed when applying this method to other systems.Ph.D.Materials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/63835/1/bpuchala_1.pd

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. Spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials